Learning is performed by optimizing the SVGB estimator with backpropagation. VAE [1]} uses centered isotropic multivariate Gaussian \(p_{\theta _{}}(\mathbf {z})=\mathcal {N}(\mathbf {z};\mathbf {0},\mathbf {I})\)  as prior of latent variable \(\mathbf {z}\) . The variational approximate posterior \(q_{\phi }(\mathbf {z}|\mathbf {x})\)  is a multivariate Gaussian with diagonal covariance matrix: \(\mathcal {N}(\mathbf {\mu },\text{diag}(\mathbf {\sigma }^2))\) , and its mean \(\mathbf {\mu }\)  and variance \(\mathbf {\sigma }^2\)  are parameterized by a neural network. For \(p_{\theta _{}}(\mathbf {x}|\mathbf {z})\) , a Bernoulli distribution for binary data or multivariate Gaussian distribution (as adopted in our model) for continuous data is often used.
